Electrotechnics: Basics

Electric field potential

Quality of field - potentiality

An important feature of the electric field, as the field has no vortices and created some stationary sources, it is a potentiality.

Electric field is called potential if the work that makes the charge carrier in such a field, while moving it in any closed loop is equal to zero.

Gravitational field of gravity is also a potential. If you lift a certain weight to a certain height and then lower it back to the surface of the Earth, in the previous point, the total mechanical work is also zero. Moreover, it does not matter at what trajectory carried raising and lowering the load. The source of the gravitational field in this example is the Land (the body with mass is many times greater than the weight of the lifted load).

Electrostatic field, ie a field that is formed by the fixed electrical charges, also has similar potentiality. The work of the charge carrier as it moves in a closed circuit in the electrostatic field will be zero. The trajectory of this movement is called closed loop, and this trajectory can be any kind of fundamental importance to its isolation, rather than the form.

Potential of electrostatic field

The figure shows the different trajectory of the charge in the electrostatic field of a plane capacitor. No matter which route moving charge (picture left), perfect their work will be the same, that is, A1=A2=A3. The right image shows the movement of charge in a closed loop. The starting and ending points of the field are the same. Charges move from point 1, then 2, 3, and arrived again at point 1, thereby forming a closed path, i.e. contour. In this case we say that he committed the mechanical work is zero.


Since the electrostatic field is a potential, in every point of space it has the potential to characterize this field. For the gravitational field it will be the gravitational potential, and for the electric - electric potential. What is the potential and how it is determined?

Potential φ points of electric field is called the work that must be expended to move the charge +q in the amount of Coulomb from infinity to this point of the field, or work on the movement of the same charge +q from that point to infinity.

From the definition of potential turns out that potential - a measure which characterizes the work of the charge, that is, it is in fact the energy characteristic of the field. What should be understood by infinity? This is still some distance, not a mathematical concept ∞. Under the infinity in determining the capacity to be understood that distance in space at which the field can be considered equal to zero, that is, field intensity in it is so small that it can be taken as zero. The lines of force of the electric field of a single charge go to infinity, and even in the infinity on the other side could meet the charge of the opposite sign, and then the two will meet infinity. Here is the meeting place is the place where the influence of the field of a single charge is zero. This place is zero potential where the potential φ=0, after the transition of the zone of zero potential of its value will change its sign. The real nature of the universe, each charge has a pair of opposite and therefore the point of infinity - is the point of equilibrium, balance.

For practical reasons it is convenient to adopt a certain line or surface (equipotential) equal to zero. This means that with respect to a source of electric field, it still has some value, but taken as a zero out of practical necessity. It turns out reasonable relative to the frame potential field. On this score there is an analogy with the gravitational field of the Earth (counting from the sea level), the effects of gravity when of the Sun is not essential, but for high orbit satellites, and should take into account the gravity of the Sun. With a significant approximation of the spacecraft to the Moon, the effect of the gravitational potential of the moon will be paramount and will require a lunar system of reference. Similarly, things and with the electric field of the Earth. If the physics of theoretical questions when considering choosing infinity, the electrical act differently and take a zero potential of the earth's surface. Accordingly, at a certain height from the surface of the Earth, in the atmosphere, the potential will have a non-zero value.

In which case, the concept of building loses its meaning? If a charge moving along different trajectories will commit different works, that is, it will depend on the shape of the path, there is the potential field does not make sense. Thus, the concept of potential refers only to the potential field.

Potential energy

The well-known in mechanics the concept of potential energy is also directed to a potential field. In the absence of a potential field can be no question of the potential energy. The potential energy of the body, we just call the work that must be expended to move the body from infinity to that point. In other words, it requires energy to to move body out of the field with zero potential in a region with high potential. Again, if the to expend a work depends on the form the way, there is no potential field, so it is impossible to speak of the potential energy.

As mentioned above, the potential - it is the characteristic of energy and hence quite easy to determine the potential energy of the potential.

Potential energy - Up is the multiplication of the charge q on the potential φ.

The equation of the potential energy electric field

Date: 01.30.2016

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© Valentin Grigoryev

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